Theorems · Theorem · order theory
le_of_forall_gt
∀ {α : Type u_2} [inst : LinearOrder α] {a b : α}, (∀ (c : α), a < c → b < c) → b ≤ a- Defined in
- Mathlib.Order.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- le_of_not_gtproof · cited by 430
- lt_irreflproof · cited by 190
Cited by19
Results whose statement or proof uses this declaration.
- infEDist_thickeningproof · cited by 3
- forall_gt_iff_leproof · cited by 3
- egauge_prod_mkproof · cited by 3
- Metric.infEDist_le_infEDist_cthickening_addproof · cited by 3
- Set.measure_eq_iInf_isOpenproof · cited by 3
- eq_of_forall_gt_iffproof · cited by 2
- egauge_pi'proof · cited by 2
- Order.IsPredPrelimit.isGLB_Ioiproof · cited by 2
- eHolderNorm_eq_zeroproof · cited by 1
- ENNReal.iInf_gt_eq_selfproof · cited by 1
- MeasureTheory.isStoppingTime_of_measurableSet_lt_of_isRightContinuous'proof · cited by 1
- le_egauge_of_forall_ne_zeroproof · cited by 1